Question

what formula is used to gain information about an individual data value when the variable is normally distributed?
$o z=\frac{x-\mu}{\sigma}$
$o z=\frac{x-\mu}{s}$
$o z=\frac{x-\mu}{\sqrt{\sigma}}$
$o z=\frac{x-\mu}{\sigma-s}$
$o z=\frac{x-\mu}{\sigma / \sqrt{n}}$

Explanation:

Step1: Recall the z - score formula for a single data point

The z - score formula for a single data value \(X\) from a population with mean \(\mu\) and standard deviation \(\sigma\) is used to standardize the value.
The formula for the z - score of an individual data value is \(z=\frac{X - \mu}{\sigma}\).

Step2: Analyze other options

• For \(z = \frac{X-\mu}{s}\), \(s\) is the sample standard deviation. This is used when dealing with a sample (not an individual data value from a population in the context of population - level normal distribution).
• For \(z=\frac{X - \mu}{\sqrt{\sigma}}\), the denominator is not the correct form of the standard deviation for a single data value.
• For \(z=\frac{X-\mu}{\sigma - s}\), this formula is not a valid statistical formula.
• For \(z=\frac{X-\mu}{\sigma/\sqrt{n}}\), this is the formula for the z - score of a sample mean \(\bar{X}\) (where \(n\) is the sample size), not for an individual data value.

Answer:

\(z=\frac{X - \mu}{\sigma}\)